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Edexcel A-Level Mathematics AS S1.2 Representation and Summary of Data Questions

Practise summarising data with diagrams and statistics, then interpreting location, spread, skewness and comparisons from evidence.

Exam points

calculate histogram bar dimensions, frequencies or estimates from class widths and areas
find or interpret means, quartiles, IQR, variance and standard deviation from data tables
use box plots or summary statistics to describe skewness, outliers and distribution shape

Covered syllabus points

S1.2.1 - Histograms, stem and leaf S1.2.2 - Measures of location – mean,S1.2.3 - Measures of dispersion – variance,S1.2.4 - Skewness

[Maximum number: 9]

The histogram shows the times taken, in seconds, by each of 260 people to complete a puzzle.

Figure for Question 1 — Edexcel A-Level Mathematics AS

(a)

Use the histogram to complete the frequency table for the times taken to complete the puzzle.

Table for Question (a) — Edexcel A-Level Mathematics AS

Given that $\sum \mathrm{f} t=11087.5$ and $\sum \mathrm{f} t^{2}=505718.75$

[ 3 ]

(b)

find an estimate for

[ 3 ]

(i)

the mean time taken to complete the puzzle,

[ 1 ]

(ii)

the standard deviation of the times taken to complete the puzzle.

[ 2 ]

(c)

Use linear interpolation to estimate the median time taken to complete the puzzle.

[ 2 ]

(d)

Describe the skewness of these data. Give a reason for your answer.

Three of the 260 people are chosen at random.

[ 1 ]

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